On Galois cohomology and realizability of 2-groups as Galois groups II

In Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 403–419] we calculated the obstructions to the realizability as Galois groups of 14 non-abelian groups of order 2 ⁿ , n ≥ 4, having a cyclic subgroup of order 2 ⁿ⁻², over fields containing a primitive 2 ⁿ⁻³th root of unity. In the present paper we obtain necessary and sufficient conditions for the realizability of the remaining 8 groups that are not direct products of smaller groups.